There are several types of pad that are marketed for keeping a rug in place over installed carpet. Most will work if the installed carpet is low-loop commercial or carpet tile, and maybe not so much if the carpet has a deeper or stiffer nap. NoMuv is the best we've tried for use with room sized rugs - grippy side up to hold the rug, slippy side down to keep the carpet nap from shoving the rug around.
WunderGrip has a product called WunderLock that works well for smaller rugs and for use on top of more problematic carpet nap. It is a felt with an adhesive that easily cleans off of the installed carpet when the rug is removed. (A lot of adhesives will leave a nasty residue, so don't go with cheap knock-offs.)
Some installed carpet will have pile too deep or too stiff for any pad to work, so don't guarantee anything.